TC 

V17 


UC-NRLF 


George  Davidson 

1RPR-1QTL 


^ 


M. 


The  Technical  Society  of  the  Pacific  Coast, 


MEASUREMENT  AND   FLOW   OF  WATER 
IN  DITCHES. 


AUG.  J.  BOWIE,  JR.,  M.  TECH.  Soc. 


GIFT 


TECHNICAL  SOCIETY  OF  THE  PACIFIC  COAST. 

INSTITUTED   APRIL,   1884. 


NOTE.— This  Society  is  not  responsible,  as  a  body,  for  the  facts  and  opinions  advanced  in 
any  of  its  publications. 

MEASUREMENT  AND  FLOW  OF  WATEK  IN  DITCHES. 

By  AUG.  J.  BOWIE,  JR.,  M.  Tech.  Soc. 

Read  June  6,  1884. 

In  California,  where  the  rainfall  over  large  portions  of  the 
State  is  small  and  periods  of  drought  of  not  uncommon  occur- 
rence, the  development  of  the  agricultural  as  well  as  the  mining 
interests,  necessarily  resulting  from  the  continued  influx  of  pop- 
ulation, will  be  dependent  greatly  upon  the  careful  husbanding 
of  the  water  supply.  The  sources  of  this  supply  are  compara- 
tively limited,  and  the  problem  of  systematic  irrigation  will  grow 
daily  in  importance  from  the  necessities  of  the  farmers;  and  the 
demand  for  water  will  steadily  increase  with  the  more  extended 
cultivation  of  the  soil. 

The  costs  of  construction  and  maintenance  of  the  necessary 
canals  and  ditches  (depending  principally  on  their  capacity)  will 
be  of  prime  importance  to  the  owners,  who  will  appreciate  fully 
the  value  of  a  correct  determination  of  the  flow  of  water.  The 
easy-going  farmer  who  purchases  the  water,  will  ultimately  dis- 
cover the  necessity  of  knowing  how  much  he  is  receiving,  and 
then  will  come  the  demand  for  a  standard  of  measurement  of 
water. 

The  history  of  northern  Italy,  from  the  fourteenth  to  the 
eighteenth  century,  is  replete  with  accounts  of  disputes  and  dif- 
ficulties arising  from  the  non-existence  of  some  accepted  stand- 
ard of  measurement  of  water.  Similar  troubles  have  arisen  at 
times  in  the  mining  regions  of  this  country,  as  can  be  attested 
by  numerous  court  reports. 


52  Bowie  on  Measurement  and  Flow  of  Water. 

With  the  experiences  of  the  past,  and  in  consideration  of  the 
future  interests  of  the  country,  it  would  seem  advisable  that  some 
uniform  gauge  and  standard  of  measurement  of  water  should  be 
adopted. 

The  miner's  inch  has  only  led  to  confusion  and  is  the  relict  of 
the  Mexican  and  Spaniard,  who  possibly  took  it  from  the  Italian. 
Like  the  Italian  oncia,  which  varied  in  nearly  every  province,  so 
its  brother  the  miner's  inch  has  followed  suit  to  even  varying  in 
the  same  district. 

In  the  construction  of  the  various  water  supply  systems  for 
the  different  placer  regions  in  this  State,  certain  experience  in 
the  measurement  and  flow  of  water  has  been  acquired,  and  it  has 
been  considered  of  sufficient  import  to  place  some  of  the  results 
of  this  work  on  record,  with  a  view  of  assisting  in  clearing  up  the 
confusion  about  the  Miner's  Inch,  and  giving  to  those  interested 
in  the  profession  the  benefits  derived  from  the  several  works. 

The  Miner's  Inch. — The  Minei's  Inch  of  water  is  a  quantity 
which  varies  in  almost  every  district  in  the  State;  no  one  gauge 
has  been  uniformly  adopted,  nor  has  any  established  pressure 
been  agreed  on,  under  which  the  water  shall  be  measured.  In 
some  counties  there  are  10,  11  or  12-hour  inches,  and  in  others 
there  is  a  24-hour  inch.  The  apertures  through  which  the  water 
is  measured  are  generally  rectangular,  but  vary  greatly  in  width 
and  length,  being  from  1  inch  to  12  inches  wide  and  from  a  few 
inches  to  several  feet  long.  The  discharges  are  through  1',  1^', 
2',  and  3-inch  planks,  with  square  or  with  square  and  chamfered 
edges,  combined  or  not,  as  the  case  may  be.  The  bottoms  of 
the  openings  are  sometimes  flush  with  the  bottoms  of  the  boxes, 
sometimes  raised  above  them.  The  head  may  denote  the  dis- 
ance  above  the  center  of  the  aperture,  or  again  that  above  the 
to£,  and  varies  from  4J  inches  to  12  inches  above  the  center  of 
the  aperture. 

The  Smartsville  inch  is  calculated  from  a  discharge  through  a 
four-inch  orifice  with  a  seven-inch  board  top;  that  is  to  say,  the 
head  is  seven  inches  above  the  opening,  or  nine  inches  above  the 
center.  The  bottom  of  the  aperture  is  on  a  level  with  the  bottom 
of  the  box,  and  the  board  which  regulates  the  pressure  is  a  plank 
one  inch  thick  and  seven  inches  deep.  Thus,  an  opening  250 


Bowie  on  Measurement  and  Flow  of  Water.  53 

inches  long  and  four  inches  wide,  with  a  pressure  of  seven  inches 
above  the  top  of  the  orifice,  will  discharge  1000  Smartsville  mi- 
ner's inches.  Each  square  inch  of  the  opening  will  discharge 
1.76  cubic  feet  per  minute,  which  approximates  the  discharge 
per  inch  of  a  two-inch  orifice  through  a  three-inch  plank  with  a 
head  of  nine  inches  above  the  center  of  the  opening,  the  said 
discharge  being  1.78  cubic  feet  per  minute.  The  Smartsville 
miner's  inch  will  discharge  2534.40  cubic  feet  in  twenty-four  hours, 
though  in  that  district  the  inch  is  only  reckoned  for  eleven  hours. 

Other  Inches. — The  miner's  inch  of  the  Park  Canal  and  Mining 
Company,  in  El  Dorado  County,  discharges  1.39*  cubic  feet  of 
water  per  minute.  The  inch  of  the  South  Tuba  Canal  Com- 
pany is  computed  from  a  discharge  through  a  two-inch  aper- 
ture, over  a  one  and  one-half  inch  plank,  with  a  head  of  six 
inches  above  the  center  of  the  orifice. 

At  the  North  Bloomfield,  Milton  and  La  Grange  mines,  the 
inch  has  been  calculated  from  a  discharge  through  an  opening 
fifty  inches  long  and  two  inches  wide,  through  a  three- inch 
plank  (outer  inch  chamfered),  with  the  water  seven  inches  above 
the  center  of  the  opening. 

2 


FIG.  1. 

Determination  of  the  inch  experiments  at  Columbia  Hill. — To 
determine  the  value  of  this  miner's  inch,  a  series  of  experiments 
was  made  at  Columbia  Hill,  latitude  39  N.,  elevation  2900 
feet  above  the  sea-level.  The  module  used  was  a  rectangu- 
lar slit  fifty  inches  long  and  two  inches  wide;  head  seven  inches 
above  the  center  of  the  opening.  The  discharge  was  over  a 
three-inch  plank;  the  outer  inch  chamfered,  as  shown  in  Fig.  1. 

'Estimated  by  J.  J.  Crawford,  M.  E. 


54  Bowie  on  Measurement  and  Flow  of  Water. 

The  size  of  the  opening  was  taken  with  a  measure  (microme- 
ter attached),  which  had  been  compared  with  and  adjusted  to  a 
standard  United  States  Yard.  Time  was  read  to  one-fifth  of  a 
second;  the  level  of  the  water  (drawn  from  a  large  reservoir)  was 
determined  with  Boyden's  hook,  micrometer  adjustment.  The 
following  results  were  obtained : 

One  Miner's  Inch  will  discharge  in  one  sec 026  cub.  ft. 

"  "  "  "        min 1.57  " 

"  "  "        hour... 94.2 

"  "  "         in  24  hours.. 2260.8  " 

The  coefficient  of  efflux  is  61.6  %.  These  figures  are  within  the 
limit  of  g-J-Q  possible  error*. 

As  the  two-inch  aperture  requires  too  much  space  for  gauging 
large  quantities  of  water,  custom  has  changed  the  form  of  the 
module,  and  an  aperture  twelve  inches  high  by  twelve  and  three- 
quarters  inches  wide,  through  a  one  and  one-half  inch  plank, 
with  a  head  of  six  inches  above  the  top  of  the  discharge,  is  now 
used.  These  openings  discharge  what  is  accepted  as  200  miner's 
inches. 

A  series  of  experiments  was  made  at  La  Grange,  Stanislaus 
County,  California,  latitude  37°  41'  N.,  elevation  216  feet  above 
the  level  of  the  sea,  to  determine  the  value  of  the  inch  thus  de- 
livered in  the  claims.  The  results  here  given  are  the  mean  of  a 
series  of  gaugings  taken  from  nine  different  apertures,  discharg- 
ing in  the  aggregate  1,800  miners'  inches. 

The  water  was  drawn  directly  from  a  flume  and  discharged 
into  a  sjnall  reservoir,  across  the  lower  end  of  which  was  fitted 
a  gauge.  The  velocity  of  the  water  issuing  from  the  flume  was 
broken  by  several  drops  as  it  entered  the  reservoir,  and  the 
gauge  at  the  lower  end  was  raised  sufficiently  to  prevent  any 
flow  due  to  an  increased  velocity  which  might  have  been  acquired 
in  the  flume. 

The  level  of  the  water  was  determined  with  a  Boyden's  hook. 

The  discharge  from  the  module  was  caught  in  a  flume  and 
conducted  to  a  box  fitted  and  leveled  for  the  purpose.  Time 
was  read  to  one-fifth  of  a  second.  The  following  results  were 
obtained : 

*The  experiments  were  made  in  1874,  by  H.  Smith,  Jr.,  C.  E. 


/V  on  *l/fasHrcint*nt  find  J:loic  of  Water.  55 

1  Miners'  inch  discharged  in  1  second 02499  cubic  feet. 

1         •  "  1  minute 1.4991 

1  "  1  hour 89.9640. 

1         '•  •«  "24  hours 2159.1460 

Effective  coefficient  of  efflux,  59.05  per  cent.* 

An  experiment  on  a  single  aperture  of  this  form,  made 
by  Hamilton  Smith,  Jr.,  gave  a  discharge  of  2179.4  cubic 
feet  per  miners'  inch  in  twenty-four  hours.  The  2230  cubic 
feet  of  the  North  Bloomfield  inch  can  only  be  considered 
an  assumed  rough  estimate  of  discharge  in  24  hours  for  1 
miner's  inch. 

The  theoretical  velocity  in  feet  per  second,  of  a  fluid  flowing 
into  the  air,  through  openings  in  the  bottoms  or  sides  of  a  vessel 
or  reservoir,  the  surface  level  of  which  is  kept  constantly  at  the 
same  height,  is  equal  to  that  which  a  heavy  body  would  acquire 
in  falling  through  a  space  equal  to  the  depth  of  the  opening  be- 
low the  surface  of  the  fluid,  and  is  expressed  as  follows: 

0=l/fyfc. 
In  which  v— velocity  in  feet  per  second. 

<7=the  acceleration  of  gravity. 

7i=the  height  fallen  in  feet. 

This  is  called  Torricelli's  theorem,  which  supposes  indefinitely 
small  orifices  with  thin  sides,  and  assumes  that  the  upper  sur- 
face of  the  water  and  the  orifices  are  under  the  same  conditions 
as  regards  atmospheric  pressure.  Conditions  and  size  of  sec- 
tional area  of  the  aperture,  friction,  resistance  of  the  air  to  mo- 
tion and  pressure  of  the  atmosphere  are  all  neglected. 

The  value  of  g  varies  in  different  latitudes,  but  for  all  practical 
purposes  is  taken  as  equal  to  32.2. 

The  theoretical  head=— 
2<7 

The  acceleration  of  gravity  at  latitude  45°=32.17  feet  per 
second,  being  represented  by  g,  for  any  other  latitude,  I. 

gf=g  (1—0.  002588  cos  2J)  f 

*The  experiments  were  made  by  the  author. 

t  See  professional  papers,  Corps  of  Engineers,  U.  S.  A.,  No.  12,  page  2€. 


56  Bowie  on  Measurement  and  Flow  of  Water. 

If  g  represents  the  acceleration  of  gravity  at  the  height,  h  and 
r  the  radius  of  the  earth,  the  acceleration  of  gravity  at  the  level 
of  the  sea  equals  — 


(r  ,     5h 
I+^ 


Flow  of  water  in  open  channels.  —  There  is  no  generally  ac- 
cepted formula  for  determining  the  velocity  of  water  in  open 
channels.  The  tables  based  on  the  old  formulas  published  prior 
to  the  works  of  D'Arcy  and  Bazin,  in  France,  and  of  Humphreys 
and  Abbot,  in  the  United  States,  being  founded  on  data  which 
ignore  the  important  factor  of  the  nature  of  the  bed  and  the 
sides  of  the  channel,  have  proved  unsatisfactory.  Hydraulic 
engineers  have  been  compelled  to  rely  for  correctness  of  calcu- 
lated result  on  the  application  of  a  combination  of  a  few  known 
laws  with  experimental  data,  which  latter,  though  all  important, 
have  been  too  restricted  for  the  deduction  of  reliable  mathe- 
matical theory. 

The  formulas,  in  terms  of  dimensions  of  cross  section  and 
slope,  are  based  upon  the  supposition  of  either  "permanent" 
or  "  uniform"  motion.  Permanent  motion  approaches  the  con- 
dition of  streams,  permits  changes  of  cross  section  and  slope  of 
the  water  surface,  excepting  sudden  bends,  causing  eddies  and 
undulations,  but  demands  that  the  discharge  from  the  different 
sections  should  be  identical.  Uniform  motion,  in  addition,  re- 
quires an  invariable  cross  section  and  constant  slope  of  the 
fluid-surface.  The  general  formulas  based  on  permanent  mo- 
tion, differ  from  those  restricted  to  uniform  motion,  "  by  taking 
into  account  changes  of  living  'force  produced  by  changes  of 
•cross  section  at  the  different  points."*  If  these  variations  are 
unknown,  the  difference  between  the  formulas  disappears. 

Chezy  considered  that  the  resistances  encountered  by  water  in 
uniform  motion  were  in  direct  proportion  to  the  length  of  the 
wetted  perimeter,  to  the  length  of  the  channel  and  to  the  square 
of  the  mean  velocity,  from  which  he  deduced  the  formula. 

*  Humphreys  and  Abbot,  Mississipi  Report,  p.  207. 


Boicic  on  Measurement  and  ]:loic  of  Water.  57 


v=c 

r  is  the  mean  velocity  in  feet  per  second. 

o  a  coefficient  taken  at  a  constant  value. 

r  the  mean  hydraulic  radius  in  feet. 

s  the  fall  of  surface  in  a  unit  cf  length. 

The  equation  indicates  the  relation  of  the  mean  velocity  to  the 
slope  and  the  mean  hydraulic  radius.  The  value  of  the  coeffi- 
cient c  has  been  demonstrated  empirically  to  have  a  wide  range. 
This  formula,  however,  has  been  considered  the  simplest,  and 
has  been  used  by  many  engineers,  different  values  being  given 
to  c,  varying  from  84  to  100  for  large  streams,  and  being  as  low 
as  68  for  small  streams.  "  Though  there  is  abundant  evi- 
dence," says  Higham  (p.  5),  "  that  the  latter  is  much  too  high 
for  low  values  of  v  in  earthen  channels,  and  that  100  is  too  low 
for  very  large  rivers,  as  high  a  value  as  254.4  having  been  de- 
duced from  the  Mississipi  observations." 

D'Arcy  and  Bazin,  by  their  experiments  on  channels  of  mod- 
erate section  with  limited  variation  of  grades,  proved  that  the 
coefficient  c  involved  not  only  r  and  s,  but  also  a  constant  for 
the  different  degrees  of  roughness  of  the  channel,  the  formula 
being  applicable  within  certain  limits  of  inclination  and  values 
of  r. 

Humphreys  and  Abbot  make  the  velocity  vary  with  the 
fourth  root  of  the  inclination,  while  Hagen  assumes  the  velocity 
to  vary  with  the  sixth  root. 

Ganguillet  and  Kutter  considered  that  the  Chezy  formula, 
v=c  i/rs~,  was  the  correct  point  of  departure,  but  that  the  co- 
efficient should  be  made  variable,  involving  not  only  r  and  s,  but 
likewise  the  degree  of  roughness  in  the  bed  or  channel. 

Ditches  in  California.  —  In  the  mining  districts  of  California 
ditches  are  constructed  boldly  with  steep  grades  and  on  irregular 
lines  with  numerous  sharp  curves.  The  cross  sections,  origi- 
nally uniform,  become  more  or  less  varied.  Absorption,  perco- 
lation, evaporation  and  leakage,  reduce  the  flow.  A  distinct 
reliable  factor  for  each  of  these  sources  of  loss  cannot  well  be 
incorporated  in  the  coefficient  of  discharge.  If,  then,  it  is 
intended  to  cover  all  of  these  common  sources  of  loss  by  such 


58  Bowie  on  Measurement  and  Flow  of  Water. 

a  coefficient,  its  value  must  be  a  material  modification  of 
values  given  commonly  in  the  text  books.  It  would  be 
certainly  an  affectation  of  accuracy  to  apply  so  complicated  a 
formula  as  that  of  Kutter  in  such  a  case,  since  the  modifying 
conditions  which  can  be  estimated  but  roughly,  call  for 
a  large  reduction  of  the  calculated  result.  This  will  be 
apparent  from  the  measurements  of  discharge  given  further 
on.  The  simple  formula,  Q=aci/rs,  expresses  more  fitly 
the  result  of  experience  in  such  cases,  wherein — 

Q — Is  the  quantity  of  water  which  the  ditch  is  capable  of 
carrying  in  cubic  feet  per  second  ? 

a — The  effective  area  of  cross  section  of  ditch  as  constructed 
originally,  in  square  feet. 

r — The  hydraulic  mean  depth  in  feet. 

s — The  fall  of  surface  in  a  unit  of  length. 

c — A  coefficient  covering  all  common  losses. 


FIG.  2.—  North  Bloomfield  Main  Ditch. 

Examples  of  value  of  Coefficient  in  Ditches. — In  its  application 
to  the  North  Bloomfield  Main  Ditch,*  (length  40  miles,  sectional 
area  23.89  square  feet,  grade  16  feet  per  mile)  with  its  abrupt 
turns  and  sinuous  course,  the  value  of  the  coefficient  c,  as  de- 
termined, varies  from  44.7  to  37.7  in  accordance  with  the  season 
of  the  year. 

The   Texas   Creekf   branch   ditch  is  about  seven-tenths  of  a 

^Increase  capacity  of  this  ditch  is  limited  by  the  pipes  across  Humbug  Canon. 
t  For  details  of  Texas  Creek  ditch  and  flume,  see  paper  by  Hamilton  Smith  Jr. ,  Trans 
actions  Am.  Soc.  C.  E.,  Vol.  XIII,  pp.  30-31. 


Bowie  on  Measurement  and  Flow  of  Water. 


59 


mile  long.  Its  sectional  area  is  13.5  feet  and  the  grade  is  20 
feet  per  mile.  The  sides  are  rough  and  the  curves  are  sharp. 
With  a  flow  of  32.8  cubic  feet  per  second,  the  ditch  runs  about 
full.  The  value  of  c=33.  In  connection  with  this  ditch  there 
is  a  rectangular  flume  2'. 67  wide  x  2'. 83  deep,  made  of  unplaned 
boards,  set  on  a  grade  of  32  feet  per  mile.  The  flume  has  some 
sharp  but  regular  curves,  and  the  water  from  the  ditch  runs  it 
nearly  full  at  these  points.  With  the  discharge  32.8  cubic  feet 
per  second,  c=59. 


FIG.  3.— Section  of  Milton  Ditch. 

On  the  Milton  line,  from  Milton  to  Eureka,  a  distance  of  19.4 
miles,  the  sectional  area  of  the  ditch  is  20.39  square  feet,  grade 
19.2  feet  per  mile  for  the  earthwork  and  32  feet  per  mile  for 
flume.  The  line  is  very  irregular,  having  many  drops  and 
chutes.  The  distance  from  Milton  to  the  measuring  box  at 
Bloody  Run  is  29J  miles.  The  minimum  established  grade  for 
the  last  10.1  miles  was  16  feet  per  mile,  with  a  sectional  area  for 
the  ditch  of  23.05  square  feet.  The  coefficient  c  determined 
from  the  gauging  at  the  measuring  box  has  varied  from  22  in  its 
leakiest  condition  to  31,  which  latter  can  be  taken  as  correct  for 
the  present  condition.  In  the  succeeding  30  miles  below  the 


60  Bowie  on  Measurement  and  Floiv  of  Water. 

gauge,  owing  to   a  better  character  of  ground,  the  coefficient 
reaches  41. 


FIG.  4.—  Section  of  La  Grange  Ditch. 

The  La  Grange  main  ditch,  17  miles  long,  has  a  sectional  area 
of  22.5  square  feet,  and  a  slope  of  7  feet  per  mile.  From  the 
delivery  at  its  Patricksville  junction  the  coefficient  c  is  determined 
to  be  52,  but  it  is  based  upon  the  assumption  that  the  depth  of 
the  canal  is  three  feet,  whereas  in  the  original  construction  it 
was  supposed  to  have  been  made  four  feet  deep,  the  discharge 
therefore  due  to  such  a  sectional  area,  would  diminish 
necessarily  the  ascribed  value  of  c*. 

In  all  these  canals,  after  the  artificial  banks  are  well  consoli- 
dated, the  water  area  is  increased  beyond  the  original  excavation 
in  the  natural  ground. 

Accuracy  cannot  be  expected  in  calculating  the  values  of  Q  for 
proposed  ditches  of  such  character.  Important  losses  must  vary 
in  every  ditch,  depending  on  the  nature  of  the  ground,  and  the 
character  of  the  construction  of  the  work  and  the  season  of  the 
year.  The  feeders  along  the  lines  compensate  largely  for  these 
losses.  In  order  to  be  safe  in  estimating  the  capacity  of  a  ditch, 
the  value  of  the  coefficient  c  for  the  dry  season  should  be  taken. 

The  following  facts  show  the  magnitude  of  the  losses  due  to 
absorption,  leakage,  evaporation,  etc. : 

Three  thousand  miners'  inches  of  water  (a  flow  of  75  cubic  feet 
per  second)  turned  in  during  the  dry  season  at  the  head  of  the 

*The  grades  given  in  all  the  above  cases,  from  which  the  different  values  of  C  were 
calculated,  exclude  the  drops,  chutes,  flumes,  etc.  Sectional  areas  represent  minimum 
cross-sectionB. 


Bowie  on  Measurement  and  Flow  of  Water.  61 

Bloomfield  ditch,  will  deliver  2700  inches  (67.5  cubic  feet  per 
second)  at  the  gauge  40  miles  distant.  Twenty-four  hundred 
inches  of  water  (60  cubic  feet  per  second)  turned  in  at  the  head 
of  the  Milton  ditch  delivered  formerly  at  the  gauge,  29J  miles 
distant,  1450  to  1600  inches  (36.25  to  40  cubic  feet  per  second), 
but  at  present  2500  inches  (62.5  cubic  feet  per  second)  turned 
into  the  head  of  the  ditch,  delivers  2000  inches  (50  cubic  feet 
per  second)  at  the  gauge.  The  exact  loss  of  water  between 
the  head  of  this  ditch  and  the  measuring  box  is  shown  in 
the  following  summary,  taken  from  the  official  records  for  the 
month  of  August  for  the  years  1875  to  1882,  inclusive.  This 
month  is  taken  as  a  dry  month,  as  prior  to  that  time  the  numer- 
ous side  streams  swell  the  amount  delivered  at  the  gauge. 

RECORD    FOR    AUGUST. 

Water  turned  at  Milton,  Water  record  at  Bloody 

Year.  24  hours,  inches.  Run,  24  hours,  inches.       Per  cent. 

1875 44,000  34,950  79.4 

1876 59,700  42,625  71.3 

1877 67,875  44,700  65.9 

1878 76,050  58,875  77.4 

1879 82,725  51,350  62.0 

1880 74,080  55,325  74.7 

1881 66,850  48,325  72.3 

1882 68,300  50,984  74.4 

The  Eureka  Lake  ditch,  with  2500  inches  turned  in  at  the  head, 
delivers  at  the  gauge,  thirty-three  miles  distant,  about  1800 
inches  in  the  dry  season. 

The  above  statistics  lead  to  the  adoption  of  values  of  the  co- 
efficient c,  varying  from  31  to  45,  in  estimating  the  capacity  of 
ditches  on  heavy  grades  of  forty  miles  length  flowing  from  sixty 
to  eighty  cubic  feet  per  second,  such  as  referred  to — that  is: 

<?=31  to  45  a  i/rST 

The  loss  incurred  in  the  distribution  of  water  is  denoted  by 
the  following  figures,  taken  from  the  official  records  of  two  mi- 
ning companies.  The  amount  received  is  measured,  at  or  near 
the  distributing  reservoirs;  the  amount  used,  at  or  near  the  pres- 


62  Bowie  on  Measurement  and  Flow  of  Water. 

sure  boxes.  The  difference  shows  the  losses  from  leakage,  evap- 
oration,  absorption,  and  wastage  arising  from  excess  of  constant 
supply  over  the  amount  needed,  with  interruptions  at  the  claim. 

NORTH   BLOOMFIELD   COMPANY    (24  HOUR   INCHES). 

Year.               Amount  Received.  Amount  Used.                              Loss. 

1870  to  1879,  inc. .       5,838,865  5,504,758  334,107  =  6  per  cent. 

1880 945,550  920,612                24,938  =  2£      " 

1881* 950,340  866,962                83,378  =  9       «' 

1882 1,025,880  1,005,977                19,903  =  2       " 

1883 862,660  836,251       26,409  =  3 


14  years 9,623,295      9, 134,560      488,735  =  5  per  cent. 

MILTON  COMPANY    (24  HOUR  INCHES). 

1882 685,933  635,884  50,049=  7  per  cent. 

1883t 446,224  361,877  84,347  =  19       •« 


2  years 1,132,157  907,761  134,396  =  13  per  cent. 


*Much  water  run  to  waste  during  4  months,  owing  to  cessation  of  work  caused  by 
litigation. 

tEnglish  reservoir  was  destroyed  June  18, 1883,  from  which  source  the  main  water 
supply  was  obtained. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


) 


LD 

AUG    *1959 

JAN     3  1978 


LD  21-100m-9,'48(B399sl6)476 


i>o/ 


OAYLORD  BROS.  If 

Syracuse,  N. Y. 
Stockton,  C.lif. 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


